The subcritical phase of 2d directed polymers (Clément Cosco, Université Paris Dauphine)

05.05.2025 16:15 – 18:00

Abstract:
Directed polymers in random environment model the behavior of a long, directed chain that spreads among an inhomogeneous environment. Dimension two turns out to be critical for the model, which then exhibits a phase transition found by renormalizing the temperature at a suitable rate (Caravenna-Sun-Zygouras 17’). In this talk, I will focus on the high temperature regime and present works in collaboration with Anna Donadini and Francesca Cottini about an elementary proof of the central limit theorem for the partition function (CSZ17) and its extension to space-correlated noise. The proof relies on a decomposition that also plays a central role in a related work with Shuta Nakajima and Ofer Zeitouni, where we study extreme value statistics of the partition function in connection to branching random walks (with a decreasing variance profile). I will try to explain this link, as well as some results about high moments estimates that we require for the proof.

Lieu

Conseil Général 7-9, Room 1-15, Séminaire Math Physics

entrée libre